If we apply the law of one price to goods in different countries, we can derive the purchasing power parity (PPP). If gold is trade in the U.S. at USD 30,000 per kilo and 1 euro costs USD 1.40, you can be pretty sure that gold will trade for around 30,000/1.4 ~ 21,400 euro per kilo. If that was not the case, there would again be arbitrage opportunities (unless there are restrictions on transporting gold across borders).
If PF is the price of a good in the foreign country, P is the price of the same good in our country and E is the exchange rate (domestic/foreign) then PPP claims that
P = PFE
The Big Mac Index
Based on PPP, the Economist regularly publishes the "Big Mac Index". PF is then the price of a Big Mac in the U.S. In February of 2009, PF was on average 3.54 USD and E = 1.28 USD/euro. According to PPP, a Big Mac should cost 2.77 euro in the euro area. In reality, it costs on average 3.42 euro. We would need an exchange rate of 3.54/3.42 = 1.04 USD/euro for the PPP to be entirely correct for the Big Mac.
According to Big Mac index, the euro is over-valued by about 24% in relation to the USD. The most expensive Big Mac, however, is found in Norway. Here a Big Mac costs USD 5.79 at the current exchange rate making the Norwegian krona overvalued by 63%.
Exchange rate determination
In PPP, PF and P denote the domestic and foreign price of a particular good. If we instead let PF and P denote price levels, we can derive the classical model of exchange rate determination simply by dividing both sides in PPP by E:
If the UK is our home country and a basket of goods costs 12.0 million UK pounds (GBP) while the exact same basket costs 14.1 million euro in France, the exchange rate, according to the classical model, ought to be 0.851 GBP/EUR or 1.175 EUR/GBP.
The exchange rate that we just calculated is often called the purchasing power adjusted exchange rate. If this was the actual exchange rate, the price levels (in the same currency) in the two countries would be the same. When we compared GDP per capita for various countries in section 3.6, it was the purchasing power adjusted exchange rate that we used to transform GDP into the same currency.
For countries where the GDP per capita is very different, the actual exchange rate is often very far from the purchasing power adjusted exchange rate. The price level in countries with a high GDP per capita is generally higher than the price level in countries with a low GDP per capita (in the same currency). It is often for services and non-transportable goods where prices deviate the most.
If the price level in the home country and the foreign price level do not change, then, according to the classical model of exchange rate determination, E will be constant. The same is true if P and PF increase at the same rate, that is, if the home country has the same inflation as the rest of the world: n = ii, where if is the rate of inflation abroad.
If, however, n > ii (P increases faster than PF), then E will increase (our currency will depreciate). For example, if n = 8% while if = 5%, P increases by 8% while the PF increases by 5% over the same period. P/PF will then be 1.08/1.05 " 1.03 times larger than the old value, that is, E will increases by about 3%. our currency will have depreciated by 3% during this period.
If itE is the rate of increase in the exchange rate (rate that our exchange rate depreciates), the classical model predicts:
ir " it – if E
The rate of depreciation is (approximately) equal to the differences in inflation between the countries. In the exercise book, we show that the exact relationship is 1 + iE = (1 + + if) and the difference between these two results is small if inflation rates are not too high.
Differences in inflation under fixed exchange rates
Suppose that we have a fixed exchange rate with the foreign country (rest of the world) but that we have different rates of inflation. Say that ii = 0 while i = 10% - our prices increase 10% annually (in our currency) while foreign prices are stable (in their currency).
If the exchange rate is fixed, domestically produced goods will the also increase by 10% per year in the foreign country. As they have stable prices, the demand for our goods will continually decline. Also, import prices in our country will remain unchanged but since the price of domestic products increase by 10% per year, imported goods will continuously become cheaper and cheaper relative to domestically produced goods and imports will increase. Such a situation is unsustainable in the long run - we will eventually be forced to devaluate our currency. To keep a fixed exchange rate between two countries, it is necessary that these countries have the same inflation.
Differences in inflation under flexible exchange rates
With flexible exchange rates, no such restriction exists - countries may have different rates of inflation and no problem with trade need to occur. To see why, imagine again that if = 0 while n = 10% (per year) but that nE = 10% as the classical model predicts. Our country has an inflation of 10% and our currency loses 10% of its value each year.
Say that Germany is our home country and that a domestically produced machine costs 10 EUR (in millions or whatever). At the same time, a foreign produced computer costs 4 USD. The exchange rate at this time is 0.711 EUR/USD. The machine will then cost 14.05 USD abroad while the computer will cost 2.85 EUR in Germany.
One year later, the price of the machine has increased to 11 EUR in Germany while the price of the computer has not changed. Also, the euro has lost 10% (E has increased by 10%) and the new rate is 0.783 EUR/USD. The price of the German machine abroad is still 14.05 USD (11/0.783) and exports will not be affected. Further, the price of the foreign-produced computer has increased to 3.13 EUR in Germany, an increase of exactly 10%. Since all other prices increase by 10% in Germany, imports will not change either.
We note that under flexible exchange rates, as long as the exchange rate depreciates at a rate equal to the difference in the rates of inflation, we may assume that exports and imports are unaffected by changes in the price levels and the exchange rate. This is exactly the assumption we have made so far.